The process and methods employed to reduce the negative effects of risk on the wellbeing of an individual, business, group or society. Identify risk Quantify risk Determine action Implement action Monitor and review it is active. It is planning, it is forward looking. The idea behind having a risk management plan is to have thought something through to begin with, identify a potential unexpected event, and have in mind a response to that, and a plan to respond to that. Managed Risks • Pure risk (“insurable” risk) • A situation in which outcomes are uncertain and involve only the potential for losses or no losses for the affected party • Speculative risk (“strategic” or “business” risk) • A situation in which outcomes are uncertain and involve the potential for losses or gains for the affected party • Speculative risks may involve zero-sum losses and gains: one party’s loss is another party’s gain Involuntary risk. The only outcome is that you experience a loss or you do not experience a loss. These are not typical risks that we take on voluntarily. Nobody is typically standing in line to take on this type of risk. The distinction between the pure risk and the speculative risk is that the only upside of the pure risk is the possibility of not having a loss. We manage the speculative risks with an emphasis on trying to maximize the likelihood of having a positive outcome or minimizing the consequences of a negative outcome. Defining Risk for Risk Management • Hubbard: Risk is a situation in which outcomes are uncertain and have potential negative consequences • Uncertainty = variation in outcome (probabilistic) • Negative consequences = involving a chance of loss Both pure risks and strategic risks are managed – with a focus on minimizing the downside (negative effects) Uncertainty and Probability Distributions • How much uncertainty we face can be quantifiably measured through identification or construction of a probability distribution of the possible outcomes • In risk management, we are concerned with losses • The probability distribution of losses represents all possible loss sizes and the relative likelihood that each will occur Comparing LossDistributions Distribution 1: Loss $0 $20,000 Loss $0 $100,000 Probability .90 .20 Probability .99 .01 Distribution 2: Which situation involves more risk? Which should receive more management attention? Should we use the same risk management approach for each situation? The first situation is riskier. 0.20 * $20,000 = $4000. 0.01 * $100,000 = $1000 The expected value of loss is higher for distribution number one, about 20% chance to $20,000 loss with an expected value of $4,000 whereas for the second distribution, the expected value of loss is only $1,000. The second situation is riskier. Another perspective on it is that $100,000 is a lot more than $20,000 and so maybe that's going to have catastrophic effects. Expected Value and Variance Factory A E(L) = .8(0) + .2(20,000) = 4,000 Var(L) = .8(0-4,000)2 + .2(20,000-4,000) 2 = 64,000,000 SD (L) = v64,000,000 = 8,000 Factory B E(L) = .99(0) + .01(100,000) = 1,000 Var(L) = .99(0-1,000)2 + .10(100,000-1,000) 2 = 99,000,000 SD (L) = v99,000,000 = 9,949.87 We square those because we don't want positive and negative differences to cancel each other out, because we want to measure the overall dispersion around the mean. The variance of loss is the dispersion around that central tendency. So the variance of loss is a weighted average of the differences between each outcome and the expected value. When we think traditionally about measuring risk, we think about expected value and that says focus on distribution number one; When we think about uncertainty, we focus on variance and that tells us focus on distribution number two; There is not a right answer. Worst Case Scenario In this situation, we need to pay more attention to distribution number two because its maximum loss is much higher. Maximum Probable Loss • MPL is a measure of the largest loss that would be “likely” to occur • “Likely” must be defined in relation to a probability of occurrence • MPL is used to characterize the extreme values of the loss distribution Losses Probability 5% • The largest consequences of risk will occur at the largest outcomes of losses MPLExample Loss ($) Probability 0 .01 500 .03 1,000 .08 2,000 .15 3,000 .20 4,000 .28 5,000 .18 10,000 .05 15,000 .014 25,000 .005 50,000 .001 What is the MPL with 98% confidence? Between $10,000 and $15,000. Use Cumulative Probability Distribution Loss ($) Probability Cumulative Probability 0 .01 .01 500 .03 .04 1,000 .08 .12 2,000 .15 .27 3,000 .20 .47 4,000 .28 .75 5,000 .18 .93 10,000 .05 .98 15,000 .014 .994 25,000 .005 .999 50,000 .001 1.00 What is the MPL with 98% confidence? when we transform the probability into cumulative probability distribution, we see that losses are less than or equal to the loss amounts that are shown on the left. Thus insurance company is not facing the same degree of uncertainty about what they have to pay out as individuals are. It does not look very risky to them because they are pooling risk across hundreds or thousands of similar organizations. So for them, the outcomes that they are going to have to pay are actually relatively certain in the aggregate. Individuals need to consider about deductibles for insurance. What are you comfortable paying for out of pocket. One should effectively transfer the bulk of risk to the insurance company. Observed Data onLosses • The number of loss events in a time period • The average events per unit of exposure is known as the average loss frequency (F) • The dollar amount of loss per accident or occurrence • The average cost per accident event is know as the average loss severity (S) • The total dollar amount of losses in a time period (T) • The average cost of losses per unit of exposure is known as the average loss (X) Frequency, Severity and Average Loss 10,000 employees per year 1,500 employee injury claims per year $3 million in employee injury costs per year • Average Loss Frequency = • Average Loss Severity = • Average Loss Costs per Employee = 1500/10000=0.15 On average, 0.15 claims per employee $3,000,000/1500 = $2000 $3,000,000/10000 = $300 Working with Observed Data • Consider a firm with 150 cars in its fleet. • It was observed that 64 of the cars experienced an accident last year (none of the cars experienced more than 1 accident) and 86 experienced no accident. • In the 64 accidents that occurred last year, 34 involved losses of approximately $3,000; 23 involved losses of approximately $12,500; and 7 involved losses of approximately $35,000. Working with Observed Data • Converting the data into a probability distribution Frequency 0 1 Estimated Probability 86/150 64/150 E(F)= Var(F)= SD(F)= Severity $3,000 $12,500 $25,000 Estimated Probability 34/64 23/64 7/64 E(S)= Var(S)= SD(S)= How to Quantify “worst-case” outcomes? Probability Total Number of Accidents What is the probability that the firm will experience more than 100 accidents in a year? =this area 100 What is the largest number of accidents the firm should expect in a “usual” year? What is the probability that the firm will experience more than 100 accidents in a year? Assume a Probability Distribution • Normal distribution: • A continuous probability distribution that is symmetric around itsmean. • This is a very common probability distribution and is often used in statistics. • When we measure things like people's height, weight, salary, opinions or votes, the graph of the results is very often a normal curve • Binomial distribution: • A discrete probability distribution of the number of successes in a sequence of n independent experiments, each with only 2 possible outcomes and with probability p of “success”. • Often used to model the number of “successes” in a sample of size n drawn with replacement from a population of size N. • E.g. Total number of accidents or events per year, where “success” = accident and p = probability of accident for any one unit Average and Total Loss Costs We can combine data on F (loss frequency) and S (loss severity) to gain insights into average losses (X). Summary Statistics: E(X) = E(F)*E(S) Var(X) = E(F)*Var(S) + [E(X)]2*Var(F) Tabulation: We can combine estimated probability distributions for F and S into a probability distribution for X Simulation: Combine observed F and S data with assumed probability distribution